It would make Harry less effective so no. I think Mab is pretty transparant about what she wants from Molly and Harry both.
Mab also seems to believe that if Harry can't measure up to her standards, then he wasn't worth it anyway, though.
Lara is clearly prohibited from killing Harry by feeding, but I am not sure "influence" is off limits - Mab probably expects Harry to be able to deal with that.
Mab would not want to lose control of Harry, but if Lara has obligations to Mab...
Although, given Starborn "mind control resistance"
can Lara enthrall him? Mab could mess with his memories in SmF, but his Starborn powers don't seem to have been "fully awakened" then.